The Mathematics of Poker

The one unrelenting fact about poker is that it is truly all about the math. There is a probability for every outcome in poker and a statistic for every hand of the poker game. Some of them are fun, some of them matter and some of them are just for MIT graduates. They are helpful to your poker game and by having a general knowledge on the mathematics of poker you put yourself in a better position to understand the game of poker over the long run.

Odds For Being Dealt Specific Hands In Texas Hold’em

The odds you will be dealt a pair of aces: 220:1

The odds you will be dealt any pair: 16:1

The odds you will be dealt AK suited: 330:1

The odds you will be dealt AK: 110:1

The odds you will be dealt either a pair or a hand with an ace: 3.91:1

Selected Odds For The Flop In Texas Hold’em

If you hold a pair, the odds against flopping a set are 7.51:1

If you hold AK, the odds against flopping either an ace or a king are: 2.08:1

If you hold a suited hand, the odds against flopping a four flush are 8:14:1

If you hold QJ, the odds against flopping an outside straight draw are 15.6:1

If you hold KQ, the odds against flopping a nut straight (AJT) are 305:1

Odds For Completing A Hand With Two Cards To Come In Hold’em

The odds against completing a four flush: 1.86:1

The odds against completing an outside straight draw: 2.18:1

The odds against completing an inside straight draw: 5.07:1

The odds against making a set by the river when you hold a pair: 10.88:1

Flopping Over Cards With Pocket Pairs In Texas Hold’em

You hold KK, the odds that no over cards will fall on the flop are: 0.29:1 (an Ace will fall about 22% of the time)

You hold QQ, the odds that no over cards will fall on the flop are: 0.71:1 ( an over card will fall about 41% of the time)

You hold JJ, the odds that no over cards will fall on the flop are: 1.32:1 (an over card will fall about 57% of the time)

You hold TT, the odds that no over cards will fall on the flop are 2.28:1 (an over card will fall about 70% of the time)

Odds For Five Card Draw Poker On The Deal

Odds that you will be dealt a pair of jacks or better: 6.69:1

Odds that you will be dealt a pair of tens or lower: 2.42:1

Odds that you will be dealt two pair: 20:1

Odds that you will be dealt three of a kind: 46.3:1

Odds that you will be dealt a straight 254:1

Odds that you will be dealt a flush: 508:1

Odds that you will be dealt a full house: 693:1

Odds that you will be dealt four of a kind: 4164:1

Odds that you will be dealt a straight flush: 64973:1

Odds For Five Card Draw Poker During The Draw Phase

If you hold one pair and draw three, your odds against making two pair or better are 2.48:1. With the same hand, your odds against making trips or better are 6.86:1

If you hold three of a kind and draw two, your odds against making a full house or better are 8.65:1

If you hold an open ended straight and draw one, your odds against completing to a straight are 4.88:1

If you hold an inside straight and draw one, your odds against completing to a straight are 10.75:1

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